Least Common Multiple (LCM) of 111 and 199
The least common multiple (LCM) of 111 and 199 is 22089.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 111 and 199?
First, calculate the GCD of 111 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 199 = 0 remainder 111 |
| 2 | 199 ÷ 111 = 1 remainder 88 |
| 3 | 111 ÷ 88 = 1 remainder 23 |
| 4 | 88 ÷ 23 = 3 remainder 19 |
| 5 | 23 ÷ 19 = 1 remainder 4 |
| 6 | 19 ÷ 4 = 4 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 180 | 1260 |
| 35 and 185 | 1295 |
| 114 and 90 | 1710 |
| 26 and 135 | 3510 |
| 39 and 24 | 312 |